Seismic surveys are used to evaluate the geometry and properties of subsurface rocks. The subsurface geometry and properties often indicate hydrocarbon deposits.
In seismic surveys, seismic energy sources are used to generate seismic signals at or near the surface of the earth. The seismic signals propagate downward into the earth and are reflected and diffracted by discontinuities in the subsurface. Some of the signals are returned back to the surface where they are detected by seismic sensors.
Seismic sensors are deployed on the surface of the earth. A seismic sensor may be a transducer that converts the seismic signals into electrical signals. The electrical signals from each sensor are transmitted and recorded for processing.
The sensors record the amplitude of the seismic signals arriving at the surface location of the sensor and also record the round-trip travel time of the signals from the seismic energy sources on the surface to a reflector and back to the surface. A display of the raw recorded signals does not provide a true picture of the reflectors in the subsurface.
The subsurface is a non-uniform medium, which causes spatial variations in the propagation velocity of the seismic signals, resulting in variations in the direction of propagation of the signals. These effects of the non-uniform medium on the seismic signals are called interferences.
At the boundaries between rock layers and faults, a part of the seismic signal undergoes reflection. The reflected signals from many reflectors arrive at the same receiver at the same time, which causes the recorded signals to appear very mixed. FIG. 1 shows recorded seismic signals that are not corrected. As will be understood by those skilled in the art, in FIG. 1, the dipping layer reflections and the fault reflection overlay each other and the subsurface structure is not resolved. As a result, the subsurface structure appears very confusing.
In seismic data processing, a numerical method known as migration is used to focus the recorded seismic signals and to move (i.e., migrate) the reflections in the seismic data to their correct spatial positions. In migrated seismic data, the locations of geological structures such as faults are more accurately represented, thereby improving seismic interpretation and mapping. FIG. 2 shows the seismic signals after migration is applied to the seismic signals shown in FIG. 1. As will be understood by those skilled in the art, the recorded signals have been moved (i.e., migrated) to the spatial location of the rock boundaries that caused the reflections. Consequently, the fault and the reflecting layers are well focused.
There are many different migration methods. Examples include: frequency domain, finite difference, and Kirchhoff migration. In general, these migration methods involve the back propagation of the seismic signals recorded at the surface of the earth to the region where it was reflected. In Kirchhoff migration, the back propagation is calculated by using the Kirchhoff integral representation. According to Kirchhoff integration, the signals recorded at the surface that originated at a given subsurface image location are summed. In order to compute the Kirchhoff integration, the travel times from the subsurface image location to each source and receiver location at the surface are required. The computation of the travel times requires a model of the seismic propagation velocity.
In existing methods, the starting seismic velocity model is determined as an independent processing step before migration. Errors in the velocity model are determined by examining the output of the migration. The velocity model is updated to correct for the measured errors and migration is applied to the data using the updated velocity model. When the errors in the velocity model have been reduced to a satisfactory level, the final migration is applied.
FIG. 3 shows the field geometry for a seismic signal generated at a single source, reflected from a single image and recorded at a single receiver, i.e., a seismic sensor. An analytical expression for the travel time of a seismic signal, t, from the source S to the image point I to the receiver G is given by,
      t    =                                                      (                                                t                  0                                2                            )                        2                    +                                                                                                          r                    ->                                    s                                                            2                                      V              rms              2                                +                      C            ⁢                                                                                                r                    s                                    ->                                                            4                                          +                                                  (                                                t                  0                                2                            )                        2                    +                                                                                                          r                    ->                                    g                                                            2                                      V              rms              2                                +                      C            ⁢                                                                                                r                    g                                    ->                                                            4                                                where    ,                  ⁢          C      =                        1          4                ⁢                                            μ              2              2                        -                          μ              4                                                                          (                                                      t                    0                                    2                                )                            2                        ⁢                          μ              2              4                                                and    ,                  ⁢                  μ        j            =                        1                                    t              0                        /            2                          ⁢                              ∑                          i              =              1                        N                    ⁢                                          ⁢                                    v              i              j                        ⁢            Δ            ⁢                                                  ⁢                          t              i                                          and, vi is the interval velocity of the seismic signal (i.e., seismic wave) of each earth layer from the surface to the depth of the image point and Vrms is the Root Mean Square (RMS) velocity of the seismic signal from the surface to the image point.
      V    rms    2    =            1              t        0              ⁢                  ∑                  i          =          1                N            ⁢                          ⁢                        v          i          j                ⁢        Δ        ⁢                                  ⁢                  t          i                    
This analytical equation for the computation of travel time of the seismic signal is a fourth order approximation. The fourth order equation provides more accurate travel times than the second order equation when the earth velocity model has a gradient increasing with depth.
An alternate method for computing the travel time of the seismic signal utilizes ray tracing. According to the ray tracing method, a table or grid of the subsurface is populated with a value corresponding to the interval velocity of the seismic signal at each point in the subsurface. As will be understood by those skilled in the art, a seismic signal is generated at the image location, and the signal is propagated through the grid using finite differences, eikonal equation solutions, or direct ray tracing using Snell's law. The transit time of the signal from the image location to each of the source and receiver locations is measured and used in the migration. Ray trace solutions account for the curvature of rays in the earth caused by the vertical velocity gradient, which produces superior quality images. Pre-computing the travel time tables provides for a significant improvement in efficiency. The travel time tables are computed and stored for later use in the imaging. Pre-computing and storing the travel time tables also allows for the inclusion of azimuth variations in the velocity.
In existing time migration methods, it is assumed that there are no azimuthal variations of the velocity. However, for geologic regimes under tectonic stress, it is well documented that azimuthal variations of the velocity exists. Fractures resulting from stress fields cause additional azimuthal variations of the velocity. In existing methods, the analysis for azimuthal variations in velocity is carried out before imaging. The recorded seismic signals are gathered in azimuth corridors according to the azimuth direction between the source location and the receiver location and then imaged using isotropic imaging. A different velocity model is used for each of the azimuth corridors. For recorded signals that have not been focused using migration, the azimuthal analysis is compromised by the mixing of signals from multiple reflection locations. In addition, the gathering of the data according to the azimuth between the surface locations of the source and receiver ignores the real propagation direction of the signal from the source to the reflection point and from the reflection point to the receiver.
Accordingly, there is a need for a seismic data processing method and system that incorporates azimuthal variations of velocity in migration of the seismic signals for improved imaging of geological structures.